Astronomy & Astrophysics manuscript no. aa28310-16
May 3, 2016
c
ESO
2016
A HIFI view on circumstellar H2 O in M-type AGB stars:
radiative transfer, velocity profiles, and H2 O line cooling
M. Maercker1 , T. Danilovich1 , H. Olofsson1 , E. De Beck1 , K. Justtanont1 , R. Lombaert1 , and P. Royer2
1
arXiv:1605.00504v1 [astro-ph.SR] 2 May 2016
2
Onsala Space Observatory, Dept. of Radio and Space Science, Chalmers University of Technology, SE-43992 Onsala, Sweden
e-mail: [email protected]
Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D 2401, 3001 Leuven, Belgium
ABSTRACT
Aims. We aim to constrain the temperature and velocity structures, and H2 O abundances in the winds of a sample of M-type Asymp-
totic Giant Branch (AGB) stars. We further aim to determine the effect of H2 O line cooling on the energy balance in the inner
circumstellar envelope.
Methods. We use two radiative-transfer codes to model molecular emission lines of CO and H2 O towards four M-type AGB stars. We
focus on spectrally resolved observations of CO and H2 O from HIFI aboard the Herschel Space Observatory. The observations are
complemented by ground-based CO observations, and spectrally unresolved CO and H2 O observations with PACS aboard Herschel.
The observed line profiles constrain the velocity structure throughout the circumstellar envelopes (CSEs), while the CO intensities
constrain the temperature structure in the CSEs. The H2 O observations constrain the o-H2 O and p-H2 O abundances relative to H2 .
Finally, the radiative-transfer modelling allows to solve the energy balance in the CSE, in principle including also H2 O line cooling.
Results. The fits to the line profiles only set moderate constraints on the velocity profile, indicating shallower acceleration profiles in
the winds of M-type AGB stars than predicted by dynamical models, while the CO observations effectively constrain the temperature
structure. Including H2 O line cooling in the energy balance was only possible for the low-mass-loss-rate objects in the sample, and
required an ad hoc adjustment of the dust velocity profile in order to counteract extreme cooling in the inner CSE. H2 O line cooling
was therefore excluded from the models. The constraints set on the temperature profile by the CO lines nevertheless allowed us to
derive H2 O abundances. The derived H2 O abundances confirm previous estimates and are consistent with chemical models. However,
the uncertainties in the derived abundances are relatively large, in particular for p-H2 O, and consequently the derived o/p-H2 O ratios
are not well constrained.
Key words. Stars: AGB and post-AGB - Stars: evolution - Stars: late-type - Stars: mass loss - Stars: abundances
1. Introduction
AGB stars play an important role in the chemical evolution of
galaxies and the universe (Busso et al. 1999; Schneider et al.
2014). Elements created inside the star get returned to interstellar
space in the form of molecules and dust grains in a wind from
the stellar surface. This mass loss is driven by radiation pressure
on dust grains formed in the upper atmosphere, which drag the
gas along through collisions (Bowen 1988; Hoefner et al. 1998;
Simis et al. 2001; Höfner 2008). The lifetime on the AGB is
determined through the mass loss.
In order to determine stellar elemental yields to interstellar space from AGB stars, and to understand their role in the
chemical evolution of the universe, it is important to determine
the molecular content of the CSE, the chemical reaction paths,
and the characteristics of the mass-loss process. Observations
of molecular emission lines have been used to determine these
properties. In particular, observations of CO emission lines have
proven to be a useful tool to describe the mass loss (e.g., Schöier
et al. 2002; González Delgado et al. 2003; Ramstedt et al. 2008;
De Beck et al. 2010; Khouri et al. 2014a). Observations of other
molecules have led to important insights in the chemistry and
structure of AGB CSEs (e.g., González Delgado et al. 2003;
Schöier et al. 2007; Maercker et al. 2008, 2009; Decin et al.
Send offprint requests to: M. Maercker
2010a; Cernicharo et al. 2010, 2011; De Beck et al. 2012; Justtanont et al. 2012; Khouri et al. 2014b; Lombaert et al. 2016).
A molecule of particular importance for M-type AGB stars
is H2 O. It is one of the most abundant molecules in the winds of
these stars, rivalled only by CO and H2 (Cherchneff 2006; Maercker et al. 2008, 2009; Decin et al. 2010a,c; Khouri et al. 2014b).
As an oxygen-bearing molecule it plays an important role in the
oxygen chemistry and the formation of other molecules. Due to
its many far infrared transitions it is a dominant coolant in the
inner CSE (Truong-Bach et al. 1999). The H2 O lines are emitted
in the warm, inner envelope, and observations of emission lines
also probe the acceleration of the wind (Decin et al. 2010a,c).
As such, observations of H2 O serve as an excellent diagnostic
for the chemistry and physics of AGB CSEs. At the same time, a
correct treatment of H2 O and its effects on the physical structure
of the CSE is essential in all radiative-transfer calculations and
mass-loss descriptions.
Observations of H2 O lines are difficult to obtain from
ground-based telescopes due to the absorption in Earth’s atmosphere (although it is possible to observe masers and vibrationally excited lines in the ν2 = 1 bending mode; Menten et al.
2006). The Infrared Space Observatory (ISO) observed a large
number of H2 O lines in the wavelength range between 43 µm
and 197 µm towards AGB stars (e.g., Barlow et al. 1996; TruongBach et al. 1999; Maercker et al. 2008). Radiative-transfer modArticle number, page 1 of 17
A&A proofs: manuscript no. aa28310-16
els generally require relatively high amounts of H2 O to fit the
observations of H2 O emission lines towards the CSEs of M-type
AGB stars. However, the ISO observations are spectrally unresolved, increasing the uncertainty in the determined H2 O abundances, and entirely eliminating any information on the velocity
field of the H2 O line emitting region. The SWAS (Melnick et al.
2000) and Odin (Nordh et al. 2003) satellites provided spectrally
resolved observations of the ground-state ortho-H2 O (110 − 101 )
transition at 557 GHz towards M-type AGB stars. Modelling the
line-width of this transition further constrained the determined
H2 O abundances, and demonstrated that the H2 O line emitting
region extends into the wind acceleration zone (Justtanont et al.
2005; Hasegawa et al. 2006; Maercker et al. 2009).
The Heterodyne Instrument for the Far-infrared (HIFI)
aboard the Herschel Space Observatory (Herschel) for the first
time provided high-sensitivity and spectrally resolved observations of a large number of H2 O lines towards AGB CSEs. The
observations used here were done as part of the HIFISTARS
guaranteed time key program (P.I.: V. Bujarrabal) to study the
CSEs around evolved stars of all chemical types, mainly targeting the CO and H2 O lines (see Sect. 2.2). In particular, HIFISTARS contained a sample of M-type AGB stars for which, in
addition to CO and H2 O, a total of seven different molecules
were detected (Justtanont et al. 2012). The HIFI observations allow us to determine the abundance and distribution of H2 O in the
CSEs of the observed sources, as well as to constrain the velocity profile, through radiative-transfer modelling of the observed
CO and H2 O lines.
In this paper we use advanced radiative-transfer models in
order to determine the abundance of H2 O in the CSEs of M-type
AGB stars, constrain the velocity profile of the stellar wind, as
well as explore the significance of H2 O line cooling in the energy
balance of the inner CSE. The basic modelling method has been
used previously for models of H2 O lines (Maercker et al. 2008,
2009), and has been upgraded to also include velocity profiles
and the effect of H2 O line cooling on the energy balance (Schöier
et al. 2011; Danilovich et al. 2014). In addition to the HIFI observations, we use spectrally unresolved lines of CO and H2 O
observed with the Photoconductor Array Camera and Spectrometer (PACS) aboard Herschel to further constrain the models. All
abundances are relative to H2 . In Sect. 2 we present the observations and basic information on the modelled M-type AGB stars.
In Sect. 3 the radiative-transfer models are presented. We present
and discuss the results in Sects. 4 and 5, respectively, and summarise our conclusions in Sect. 6.
2. Observations
We model rotational lines from the main isotopologues of CO
and H2 O from both ground-based and space telescopes. The observations have been published previously, and are summarised
below.
2.1. Ground-based observations of CO
We included ground-based observations in the molecular line radiative modelling of CO. The observations were taken at Onsala
Space Observatory, the JCMT, and SEST (for details, see Kerschbaum & Olofsson 1999; González Delgado et al. 2003; Justtanont et al. 2005; Ramstedt et al. 2008; Maercker et al. 2008,
and Table A.1). Transitions from CO(1 − 0) to CO(4 − 3) were
included for all sources except R Dor, which lacks CO(4−3). The
uncertainty in the integrated intensities is assumed to be 20%.
Article number, page 2 of 17
2.2. HIFI observations of CO and H2 O
The HIFI observations covered a number of expected strong CO
and H2 O lines in the frequency range 556.6–1843.5 GHz. For
CO the CO(6 − 5), CO(10 − 9), and CO(16 − 15) were observed.
The observed integrated intensities for CO and the observed H2 O
lines are presented in Tables A.1 to A.3. These observations were
already presented in Justtanont et al. (2012), but were reprocessed using the latest main beam efficiencies. For some of the
bands this led to an increase in the integrated fluxes of up to 20%.
We assume an average uncertainty in the integrated intensity for
all lines of 20%.
2.3. PACS observations of CO and H2 O
The PACS observations were taken as part of the MESS
guaranteed-time key project (Groenewegen et al. 2011), which
covered a sample of AGB stars of all chemical types. The observations and the detailed data reduction will be presented in
a forthcoming paper dedicated to the M-type AGB stars of the
MESS sample (Decin et al. in prep). The PACS spectra cover
the entire frequency range from 1580 up to 5450 GHz. For this
study, we only include non-blended CO and H2O emission lines.
For a detailed description on how line blends are identified, we
refer to Lombaert et al. (2016). The observed integrated intensities are presented in Tables A.1 to A.3. We assume an average
uncertainty in the integrated intensity for all PACS lines of 20
2.4. Sources
The HIFISTARS program included nine M-type AGB stars. Of
these we include only fours stars: R Dor, R Cas, TX Cam, and
IK Tau. R Dor is a SRb variable, and the remaining sources are
Mira-type variables. The HIFI observations of IK Tau were modelled by Decin et al. (2010c) using a different radiative-transfer
code. We include IK Tau here for a comparison of the modelling
approaches. The HIFI observations of W Hya were modelled in
detail by Khouri et al. (2014a,b) using the same code as Decin
et al. (2010c). Mira has a very complex circumstellar environment due to binary interaction (Ramstedt et al. 2014), and the
remaining sources are OH/IR stars with high mass-loss rates.
These sources are therefore not included in this study.
The mass-loss rates and H2 O abundances of the remaining
sources have been modelled previously (Maercker et al. 2008,
2009). The lowest and highest mass-loss rates of the sample were
estimated to be 2 × 10−7 M yr−1 (R Dor) and 1 × 10−5 M yr−1
(IK Tau), respectively, based on ground-based CO observations
only. Ortho-H2 O abundances were estimated to be between
2.0 × 10−4 (R Dor) and 3.5 × 10−4 (IK Tau) relative to H2 , based
on ISO observations. For the Mira-variables R Cas, TX Cam and
IK Tau the luminosities were derived from a period-luminosity
relation (Feast et al. 1989) and the distances were derived in the
dust modelling, while for the SRb variable R Dor we assumed
a distance of 59 pc and derived the luminosity in the dust modelling. The same procedure was used in Maercker et al. (2008).
3. Radiative-transfer modelling
The radiative-transfer modelling is done by combining results
from models of the dust radiation field, CO radiative-transfer
models, and H2 O radiative-transfer models. All models assume
a spherically symmetric, homogenous wind produced by a constant mass-loss rate. The procedure allows us to determine the
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
dust temperature profile, the mass-loss rate, the kinetic temperature profile, the gas expansion velocity profile, and the fractional H2 O abundance (relative to H2 ) distribution throughout
the CSE. Since the aim of the paper is to compare the derived
H2 O abundances between the sources, derive gas-velocity profiles, and investigate the significance of H2 O line cooling, we
treat the sources as homogenously as possibly. Therefore basic
properties, such as the dust grain sizes, dust composition, and the
initial wind velocity, are assumed to be the same for all sources.
Although detailed modelling of these parameters for individual
sources may result in different values, the uncertainties in these
individual models would complicate the comparative study that
is the goal of this work. This basic modelling strategy has been
thoroughly tested and used previously (e.g., Schöier & Olofsson
2001; Olofsson et al. 2002; Ramstedt et al. 2008; Maercker et al.
2008, 2009; Schöier et al. 2011; Danilovich et al. 2014).
3.1. The basic CO model
The code used for the modelling of the CO lines is described in
detail in Schöier & Olofsson (2001). It employs the Monte Carlo
method and is a non-local, non-LTE radiative-transfer code that
solves the energy balance and derives a self-consistent kinetic
temperature profile. We include radiation from dust by calculating the spectral energy distribution using DUSTY (Ivezić et al.
1999), constrained by 2MASS and IRAS fluxes. We used amorphous silicate dust with optical constants from Justtanont & Tielens (1992), assuming spherical grains with a radius of 0.05 µm
and a density of 3 g cm−3 . The dust model calculates the dust
condensation radius, the dust optical depth, τd , at 10 µm and
gives a dust temperature profile, both of which are included in
the CO model. Our dust models are largely based on the results
presented in Maercker et al. (2008), with possible slight adjustments in the luminosity and/or dust optical depth. The radius of
the CO envelope is determined by models of photodissociation
of CO (Mamon et al. 1988). The code and modelling method has
been used extensively to model the emission lines from various
molecules, including CO (e.g., Olofsson et al. 2002), SiO (Ramstedt et al. 2009), and HCN (Schöier et al. 2013).
Models of CO lines up to the J = 4 − 3 transition were used
to determine the basic properties of the CSE in the modelling
of H2 O lines observed by ISO and Odin (Maercker et al. 2008,
2009). The emission of these lines is dominated by the outer
parts of the envelope, where the wind has already reached its terminal velocity. HIFI provides new observations of higher-energy
CO transitions. These are emitted in the inner CSE, and it is now
possible to constrain the velocity profile. The models describe a
velocity law for the gas and the dust separately. The gas-velocity
profile follows the form
Ri β
υg (r) = υg,i + (υg,∞ − υg,i ) × 1 −
,
r
(1)
where υg,i is the gas expansion velocity at the inner radius (assumed to be 3 km s−1 in all models), υg,∞ is the gas terminal velocity, Ri is the inner radius (set to the dust condensation radius),
and β describes how fast the wind accelerates. The dust expansion velocity is connected to the gas expansion through the dust
drift velocity υdr (r):
υd (r) = υg (r) + υdr (r),
(2)
where υdr (r) follows the same shape as Eq. 1, with υdr,i the drift
velocity at the inner radius. The terminal drift velocity υdr,∞ is
calculated by
r
υdr,∞ =
L υg,∞ Q
Ṁc
,
(3)
where L is the stellar luminosity, υg,∞ is the terminal gas expansion velocity, Q is the scattering efficiency assumed to be 3%,
Ṁ is the mass-loss rate, and c is the speed of light. The terminal dust velocity is then given by υd,∞ = υdr,∞ + υg,∞ . Note that
there are no constraints on the dust velocity profile, and we assume Eqs. 2 and 3 to give reasonable values. However, the exact
shape of the drift velocity profile strongly affects the heating in
the inner envelope (see Sect. 3.3).
The gas expansion velocity at the inner radius, υg,i , equals
typical values of the sound-speed in the inner winds of AGB
stars (e.g., Decin et al. 2006). The gas-velocity profile is constrained by fitting the widths of the CO lines at the zero-intensity
level. Low-J lines constrain the terminal velocity, while higher-J
lines are emitted from closer to the star and constrain the shape
of the expansion profile. This is not affected very much by the
adopted mass-loss rate, and the expansion velocity profile can be
constrained by initially assuming reasonable parameters for the
mass-loss rate. We base our initial values on previous models of
CO lines for these sources assuming constant expansion velocities. Once the new expansion velocity profile is determined, we
proceed to model the mass-loss rate and temperature profile of
the CSE to include in the H2 O modelling. The best-fit CO model
is determined by calculating a grid of models varying the massloss rate and dust-to-gas ratio. To find the best fit to the data, a χ2
analysis comparing the observed line intensities with the model
intensities is then performed by minimising
X Iobs,i − Imod,i !2
χ =
,
σobs,i
2
(4)
where Iobs,i is the integrated intensity of the observation i, Imod,i
is the modelled intensity, σobs,i is the uncertainty in the observation. An error of 20% in the integrated intensities is assumed for
all the CO lines.
3.2. The basic H2 O model
We use an accelerated lambda iteration (ALI) method to calculate the radiative transfer of H2 O lines. The model is the same
as described in Maercker et al. (2008), but now includes a velocity profile in the same form as Eq. 1. We include the same
dust-radiation field and velocity profiles as for CO. The massloss rate and kinetic temperature profiles are included from the
results of the CO modelling. The remaining free parameters in
the H2 O models are the fractional H2 O abundance at the inner radius and the e-folding radius of the H2 O envelope (see Maercker
et al. 2008). Together these describe the fractional abundance
distribution of H2 O. We model both ortho- and para-H2 O. The
best-fit H2 O model is found by performing the same χ2 analysis as for CO, but now on a grid of models in H2 O-abundance
and radius of the H2 O envelope. An error of 20% is assumed for
the integrated intensities of the HIFI and PACS lines. A good
estimate of the H2 O radius is obtained from photodissociation
models as the radius where the OH abundance peaks (as a photodissociation product of H2 O; Netzer & Knapp 1987; Maercker
Article number, page 3 of 17
A&A proofs: manuscript no. aa28310-16
et al. 2008, 2009). From here on, we will refer to the photodissociation radius of H2 O as RNK , given by
RNK

0.7
!
υg,∞ −0.4
 Ṁ 
= 5.4 × 10  −5 
cm.
km s−1
10
16
(5)
3.3. Heating and cooling in the energy balance: the problem
of H2 O line cooling
The CO model self-consistently solves the energy balance
throughout the CSE by including all (known) heating and cooling terms (Schöier & Olofsson 2001). The effect of heating due
to dust-gas collisions, photoelectric heating, and heat exchange
between the dust and the gas is included. The total cooling includes cooling due to adiabatic expansion, and molecular line
cooling from CO and H2 . In order to determine the effect of
H2 O line cooling on the energy balance in the inner CSE, the
contribution to the cooling by H2 O lines is given as output in the
H2 O model. This can be included in the energy balance when
calculating the CO model.
To fully include H2 O line cooling, a careful iterative procedure is necessary, slowly increasing the contribution from H2 O
line cooling in each step. Immediately including full H2 O line
cooling typically leads to over-cooling in the inner envelope and
results in negative temperatures. This iterative procedure was
followed previously for the S-type stars χ Cyg and W Aql using
HIFI data as constraints (Schöier et al. 2011; Danilovich et al.
2014, respectively).
In the case of M-type AGB stars, the abundance of H2 O is
high enough to make it one of the dominant sources of cooling,
in particular in the inner envelope. Here we attempt to include
H2 O line cooling in an iterative procedure for the M-type stars
R Dor and R Cas. We start from the best-fit CO model that does
not include H2 O line cooling. The kinetic temperature profile,
velocity profile, and mass-loss rate are included as input in the
H2 O models. The abundance of H2 O is then adjusted to fit the
observed HIFI and PACS lines, and the H2 O line cooling is calculated (see Sect. 5.1 for details). Only a fraction of the resulting
H2 O line cooling is then included in the CO model. This allows
us to adjust the CO model in a way that counteracts extreme
cooling and to ensure that the model still fits the observations
by, e.g., increasing the mass-loss rate, increasing/decreasing the
dust-to-gas ratio, and adjusting the drift-velocity profile. Once
a new satisfactory CO model has been calculated, a new H2 O
model is calculated based on the new parameters, giving a new
H2 O abundance and hence cooling function. This procedure is
repeated, increasing the fraction with which H2 O line cooling is
included with every step. Full H2 O line cooling is included when
100% of the cooling function is included in the energy balance,
good fits have been obtained to the observed lines for both CO
and H2 O, and the temperature profile has converged between iterations.
While this procedure was successful for the S-type stars, we
come to the conclusion that it is not feasible for the high H2 O
abundances in M-type AGB stars. The iterative procedure makes
the modelling very computationally expensive. It is therefore unfeasible to run a grid of models to properly probe parameter
space, making the model results very unreliable. For the same
reason the H2 O e-folding radius is treated as a fixed parameter
and is set to RNK . We nevertheless attempted to include 100%
H2 O line cooling for the low mass-loss-rate objects R Dor and
R Cas and find that either a complete understanding of the heating and cooling processes in the CSE is lacking, or that the nuArticle number, page 4 of 17
merical implementation of radiative line cooling may have to
be revised (see Sect. 5.1). Although a sufficient number of COlines nevertheless constrain the temperature profile of the CSE,
a correct treatment of H2 O line cooling is necessary for a full
understanding of the physical processes in the CSEs of M-type
AGB stars. Consequently the final CO and H2 O models do not
include H2 O line cooling.
Note that Decin et al. (2010b) do manage to include H2 O line
cooling in the energy balance for the M-type AGB star IK Tau.
However, they do not include any explicit discussion on the issues of H2 O line cooling, and it is not clear how they avoid the
problems with the energy balance that we encounter in our modelling.
4. Results
4.1. CO models
Figure 1 shows the best-fit CO models compared to the observed
ground-based and HIFI lines for R Dor. Figures A.1 to A.3 show
the equivalent for R Cas, TX Cam, and IK Tau, respectively. Table A.1 gives the observed and modelled integrated intensities of
all CO lines, including the PACS lines, together with the upperlevel energies (Eup ) and the ratios between models and observations for individual lines (∆). Fig. 2 shows the χ2red maps for the
different CO model grids and Table 1 gives the best-fit parameters. The integrated intensities of the individual observed lines
are all reproduced to within ≈25%. The average ratios between
all observed and model lines (δ) are all close to 1. Although observed by HIFI, the CO(16 − 15) transition towards TX Cam is
extremely over-estimated in the model by an order of magnitude,
while the PACS line is well reproduced. The HIFI line is therefore excluded in the χ2 analysis. The ratio between modelled and
observed line intensities as a function of Eup is shown in Fig. 3
(red crosses). Generally the lines scatter around a ratio of one,
although there might be a slight correlation, with models preferentially under-predicting the intensities for low-Eup transitions.
For all models we use the photodissociation radius described
by Mamon et al. (1988). This generally leads to overly resolved
model line-profiles for the lower transitions, as evidenced by
the double-peaked model line-profiles (specifically discussed for
R Dor by Olofsson et al. 2002). This is a common problem in
CO radiative-transfer models (e.g., Justtanont et al. 2005; Maercker et al. 2008; Danilovich et al. 2015). We attempted to fit the
low-J line profiles by reducing the CO envelope size. However,
this generally leads to an underestimation of the total integrated
intensity compared to the high-J transitions. A possible way of
correcting for this is by changing the dust parameters and the
velocity field. However, the angular size of the envelope also depends on the assumed and uncertain distance to the source. Since
this is a degenerate problem, we chose to fix the radius to the CO
photodissociation radius and use the integrated intensities when
determining the best-fit models.
In principle the terminal expansion velocity of the gas, υg,∞ ,
should be well constrained by the width at zero power (in the following referred to as the width of the line) of the low-J CO transitions, while the widths of the higher-J CO transitions and H2 O
transitions constrain the shape of the velocity profile (β in Eq. 1).
We attempt to constrain the velocity law using the observed CO
and H2 O lines, adjusting β in the radiative-transfer models to
fit the observed line widths. For R Cas we derive β = 2.5, and
for the remaining three sources β=1.5. For IK Tau the momentum equation gives a steeper profile with β = 0.6 (Decin et al.
2010c). Although comparatively shallow velocity profile seem to
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
CO(2-1), ∆ : 0.9
4
mb
0.4
T
0.2
0
CO(6-5), ∆ : 0.7
1.5
6
3
T mb [K]
[K]
0.6
T mb [K]
CO(3-2), ∆ : 1
8
2
1
T mb [K]
CO(1-0), ∆ : 1.1
4
2
0
0
-10
0
10
velocity [km/s]
-10
0
10
velocity [km/s]
CO(10-9), ∆ : 0.9
CO(16-15), ∆ : 1.2
1
0.5
0
-10
0
10
velocity [km/s]
-10
0
10
velocity [km/s]
2
1.5
T mb [K]
T mb [K]
1.5
1
0.5
1
0.5
0
0
-10
0
10
velocity [km/s]
-10
0
10
velocity [km/s]
Fig. 1. Best-fit CO models for R Dor. The blue histograms are the observations. The red lines are the model lines, the green lines are the model
lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the 3LSR = 6.5 km s−1 .
be preferred, the β is not very well constrained by the observed
CO and H2 O lines (Fig. 4), and we estimate the uncertainty in β
to be ±1.
R Dor the profiles can be described well by power laws of the
form
The estimated mass-loss rates are consistent with previous estimates using the same radiative-transfer code and based
on ground-based data alone (Maercker et al. 2008). Only for
TX Cam do we derive a mass-loss rate a factor of ≈2 higher than
the previous estimate − still within the absolute uncertainty of
independent mass-loss rate estimates of a factor of three (Ramstedt et al. 2008). The uncertainty in the mass-loss rate within the
adopted model is ≈30%. For IK Tau it proved difficult to find an
upper limit to the mass-loss rate, likely due to a saturation effect
of the CO lines at high mass-loss rates, caused by increasing line
optical depths and cooler envelopes (Ramstedt et al. 2008). See
Sect. 5.5 for a comparison with similar codes.
r
T (r) = T i ×
Ri
The derived dust-to-gas ratios have considerable uncertainties. For R Dor and R Cas we derive values of a few times 10−4
with relatively strong constraints on the upper limit. For TX Cam
we derive a value a factor ≈50 larger. For IK Tau the best-fit
value is ≈10 times larger than for R Dor and R Cas, and agrees
with chemical models at 6 R∗ (Gobrecht et al. 2016), however no
limits can be set. Ramstedt et al. (2008) derive values of a few
times 10−3 . The dust-to-gas ratio mainly affects the energy balance, where it is part of the heating of the gas through dust-gas
collisions. This heating term depends degenerately also on the
grain size and density. For this reason Schöier & Olofsson (2001)
chose to combine these parameters in the so-called h-parameter.
The derived d/g-ratios give h-parameters of 0.05, 0.03, 1.7, and
0.3 for R Dor, R Cas, TX Cam, and IK Tau, respectively. Ramstedt et al. (2008) derive values of 1.0 and 0.3 for TX Cam and
IK Tau, respectively.
Finally, the kinetic temperature profiles are shown in Fig. 5.
Note again that although the energy balance is solved in the CO
models, the contribution from H2 O line cooling is not included
in any of the models (see Sect. 3.3). For TX Cam, R Cas, and
!α
,
(6)
where T i is the temperature at the inner radius Ri . The exponents
α are between −0.6 and −1.0. For the low mass-loss-rate M-type
AGB star W Hya Khouri et al. (2014a) derive an exponent of
−0.65 ± 0.05. In models of the chemical network in the CSE of
AGB stars, Willacy & Millar (1997) use α = −0.6 for R Dor,
TX Cam, and IK Tau.
Our profile for IK Tau deviates more from a simple power
law in the inner and outermost parts of the CSE, but can generally be fit with α = −0.98. Solving the energy balance including
H2 O line cooling in the modelling of CO lines towards IK Tau,
Decin et al. (2010b) derive a temperature profile consistent with
an exponent of −0.6, significantly different from our value. Their
derived mass-loss rate is ≈50% higher than our value, and they
use a dust-to-gas ratio a factor four higher. These values lie
within the uncertainties quoted here and in Decin et al. (2010b),
and it is not clear why there is a difference in temperature profile
and whether this is related to the H2 O line cooling.
4.2. H2 O models
Figure 6 shows the best-fit ortho-H2 O and para-H2 O models for
the HIFI lines compared to the observed lines for R Dor. Figures A.4 to A.6 show the equivalent for R Cas, TX Cam, and
IK Tau, respectively. Tables A.2 and A.3 list the same parameters as Table A.1, but for the HIFI and PACS lines of ortho-H2 O
and para-H2 O, respectively. Figure 7 shows the χ2red -maps for
ortho-H2 O and para-H2 O for all objects. We indicate both the
best-fit radius in the grid, as well as the best-fit H2 O abundance
using the radius determined by Netzer & Knapp (1987), RNK .
It is not possible to set upper limits to the H2 O radii. The H2 O
Article number, page 5 of 17
A&A proofs: manuscript no. aa28310-16
Table 1. Stellar parameters and results of the SED and CO line-emission models. T∗ and L∗ are the stellar effective temperature and luminosity,
respectively. Ri is the inner radius from which the CSE is modelled, and T i the temperature at the inner radius. D is the distance to the source. τd
is the dust optical depth at 10 µm, υ∞ the terminal gas expansion velocity, β the exponent of the velocity law, d/g the derived dust-to-gas ratio, Ṁ
the gas mass-loss rate, Re the CO-photodissociation radius, δ the average ratio between integrated model and observed line intensities, and χ2red the
reduced χ2 value of the best-fit model.
Source
R Dor
R Cas
TX Cam
IK Tau
T∗
[K]
2400
1800
2400
2100
L∗
[L ]
6500
8725
8600
7700
Ri
[10 cm]
6.6
25
30
18
Ti
[K]
1680
1050
845
960
13
mass-loss rate [10-7]
R Dor
D
[pc]
59
172
380
265
τd
0.05
0.09
0.4
1.0
υ∞
[km/s]
5.7
10.5
17.5
17.5
β
1.5
2.5
1.5
1.5
d/g
[10−2 ]
0.08
0.04
2.6
0.5
Ṁ
[10 M ]
1.6
8.0
40
50
−7
Re
16
[10 cm]
1.6
3.2
6.6
7.5
δ
χ2red
1.0
0.9
0.9
0.9
0.65
1.7
3.1
2.9
R Cas
0.5
12
2
R Dor
10
1.5
0
8
-0.5
1
6
0
0.2
0.4
0.6
500
1000
1500
2000
0.5
4
0.5
0
R Cas
0
1
2
3
obs mod
80
60
40
20
0
5
dg-ratio [10-2]
10
/I
140
120
100
80
60
40
100
log[∆ (I
mass-loss rate [10-7]
IK Tau
)]
0
TX Cam
-0.5
dg-ratio [10-2]
Fig. 2. χ2 -maps of the CO model grids for R Dor (top left), R Cas (top
right), TX Cam (bottom left), and IK Tau (bottom right). The contours
show the 1σ, 2σ, and 3σ levels. The cross marks the lowest χ2red model.
500
1000
1500
2000
TX Cam
0
-0.5
0.2 0.4 0.6 0.8
0
0.5
0
500
1000
1500
2000
0.5
IK Tau
0
-0.5
0
500
1000
1500
2000
Eup [K]
line emitting region is limited by radiative excitation, and the
H2 O lines hence do not probe the outer regions very well. In all
cases RNK is consistent with the best-fit radius when allowing
R to vary freely, and we use this radius for the H2 O envelope.
All model results refer to models using RNK . Table 2 gives the
best-fit values for the abundance, the average ratios between all
integrated model and observed line intensities (δ), and the χ2red
values. The dependence of the model and observed line ratios on
the upper level energy Eup is shown in Fig. 3. As with the CO
lines, the scatter lies around one, with a slight under-prediction
by the model lines. However, no clear trend with Eup can be seen.
The derived ortho-H2 O abundances lie between ≈10−5 –10−4
relative to H2 . For R Dor and R Cas this is significantly lower
than previously derived values based only on ISO observations (Maercker et al. 2008). Including the spectrally resolved
557 GHz line observed with Odin required a reduction of the
(constant) expansion velocity to fit the observed line-width, and
led to a slight reduction in the ortho-H2 O abundance for R Dor,
albeit well within the uncertainties (Maercker et al. 2009). Including a velocity profile forces a significant reduction of the
H2 O abundance to reproduce the observed intensities. ObserArticle number, page 6 of 17
Fig. 3. Ratio between observed and modelled integrated intensities vs.
upper-level energy for the different transitions (CO: red crosses, orthoH2 O: blue dots, para-H2 O: green circles).
vations of several para-H2 O lines allow us to set constraints
on the para-H2 O abundances and derive ortho/para-H2 O ratios
(o/p-ratio). The uncertainties in the derived abundances lead to
considerable uncertainties in the derived o/p-ratios. This is especially true for TX Cam, where the low number of observed
para-H2 O lines leads to a bad fit to the observations with the
by-far highest χ2red value.
5. Discussion
5.1. The significance of H2 O line cooling
The current implementation of H2 O line cooling in the radiativetransfer codes implies that line cooling by H2 O significantly affects the temperature in the inner envelope of M-type AGB stars
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
Table 2. Results of the H2 O modelling. The H2 O abundances are given relative to H2 . The values in brackets give the 1σ ranges.
Source
RNK
[×1015 cm]
1.4
3.6
9.0
11
R Dor
R Cas
TX Cam
IK Tau
f(o-H2 O)
[×10−4 ]
2 (0.7 – 5.6)
0.6 (0.4 – 0.9)
0.3 (0.2 – 1.0)
3.5 (1.1 – 5)
δ
χ2red
0.9
0.8
0.6
0.8
1.11
1.9
3.9
1.8
R Dor
6
4
2
0
13.5
14
14.5
15
15.5
16
16.5
17
R Cas
10
v(r) [km/s]
5
0
14
14.5
15
15.5
16
16.5
20
17
TX Cam
10
0
14
14.5
15
15.5
16
16.5
17
20
17.5
IK Tau
10
0
14
14.5
15
15.5
16
16.5
17
17.5
log(radius) [cm]
Fig. 4. Velocity profiles derived for R Dor, R Cas, TX Cam and IK Tau
(top to bottom) compared to the measured line-widths from lines emitted at different radii in the CSE (CO: red crosses, ortho-H2 O: blue dots,
para-H2 O: green circles. The widths are measured at zero power. The
radii are determined by the peak in the brightness profiles of each transition). The solid black lines give the profiles with the β given in Table 1,
the dotted black lines give the profile for β = 0.6.
R Dor
R Cas
log(T) [K]
3
-0.83
-0.91
2
2
1
1
14
15
16
log(R) [cm]
17
TX Cam -0.62
IK Tau -0.98
3
14
15
16
log(R) [cm]
f(p-H2 O)
[×10−4 ]
0.5 (0.2 – 0.7)
0.2 (0.1 – 0.3)
0.03 (0.01 – 0.04)
0.7 (0.2 – 1.3)
δ
χ2red
o/p-ratio
1.0
1.0
0.7
0.9
1.0
1.6
6.7
1.2
4 (1 – 26)
3 (1 –9)
10 (5 – 100)
5 (0.8 – 25)
(at radii Ri < r < a few Ri ). The energy balance in this inner
part of the CSE is very sensitive to the amount of H2 O line cooling included in the model, quickly leading to extreme cooling.
Models of the S-type stars χ Cyg and W Aql, that include H2 O
line cooling, had H2 O abundances factors 2 − 35 lower than the
abundances estimated for the M-type stars here (Schöier et al.
2011; Danilovich et al. 2014). For our high mass-loss-rate objects, H2 O line cooling is too strong to be included in the energy balance. For R Dor and R Cas we nevertheless managed
to include 100% H2 O line cooling. While the iterative procedure
does not allow us to realistically calculate a grid of models due to
computational limitations, the resulting fit to the observed lines
gives similar χ2red values to the models without H2 O line cooling.
The derived mass-loss rates and H2 O abundances do not change
significantly between models with and without cooling, since the
observed CO lines effectively constrain the temperature profile.
However, to balance the additional cooling in the inner envelope
the d/g ratio needs to be increased by a factor of approximately
two. Much more importantly, the only way we managed to include full H2 O line cooling was to change the drift-velocity profile from starting low and increasing with radius to starting high
and decreasing with radius. This changes the dust-velocity profile to a constant value throughout the entire CSE. Although the
dust velocity profile and the drift velocity are not constrained
observationally, theoretical models of dust-driven winds generally predict very low drift velocities between the dust and the
gas for high mass-loss rates, and increasing drift-velocity with
increasing distance (as assumed in this paper), or a constant drift
velocity. A situation where the dust velocity is constant throughout the envelope therefore seems unphysical.
A constant dust velocity drastically increases the heating due
to the dust-gas interaction in the inner CSE, and hence balances
the cooling due to H2 O. While this scenario is unrealistic, it indicates that some physics leading to heating in the inner envelope
may be missing. Since the dust-velocity profile is not constrained
by observations, changing the profile in an ad hoc manner becomes similar to adding an arbitrary heating term to counterbalance the cooling by H2 O. We have no suggestion as to what
this additional heating may be, or whether this indicates a fundamental problem in our understanding of the physics in the inner
CSEs of AGB stars.
Another possible explanation for the problem of extreme
H2 O line cooling is the way the line cooling is calculated. In
the current version of the radiative transfer, the contribution due
to line cooling (for any molecule) is included following Sahai
(1990):
17
Fig. 5. Kinetic temperature profiles (solid lines) calculated in the energy
balance of the CO modelling for R Dor (left panel, blue), R Cas (left
panel, red), TX Cam (right panel, blue), and IK Tau (right panel, red).
The dashed lines show power-law fits to the individual profiles (Eq. 6).
The numbers give the exponents for the respective fits.
Cline (r) =
X
∆Eul kB (pl clu − pu cul ),
(7)
l,u>l
where ∆Eul is the energy difference of a transition from upper
level u to lower level l, kB the Boltzmann constant, pl and pu the
lower and upper level population densities, and clu and cul the
collisional excitation and de-excitation rates from the lower to
Article number, page 7 of 17
A&A proofs: manuscript no. aa28310-16
o-H 2O(3 12-3 03), ∆ : 0.7
0.5
T mb [K]
1
o-H 2O(3 21-3 12), ∆ : 0.7
8
2
T mb [K]
T mb [K]
1.5
o-H 2O(3 12-2 21), ∆ : 1.3
1
T mb [K]
o-H 2O(1 10-1 01), ∆ : 0.7
6
4
2
1
2
0
0
0
0
-20
0
20
velocity [km/s]
-20
0
20
velocity [km/s]
p-H 2O(1 11-0 00), ∆ : 0.7
-20
0
20
velocity [km/s]
p-H 2O(4 22-4 13), ∆ : 0.9
-20
0
20
velocity [km/s]
p-H 2O(6 33-6 24), ∆ : 1
1
1
2
T mb [K]
T mb [K]
T
mb
[K]
4
0.5
0.5
0
0
0
-20
0
20
velocity [km/s]
-20
0
20
velocity [km/s]
-20
0
20
velocity [km/s]
Fig. 6. Best-fit o-H2 O and p-H2 O models of the HIFI Lines for R Dor. The blue histograms are the observations. The red lines are the model lines,
the green lines are the model lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the 3LSR =
6.5 km s−1 .
upper and upper to lower levels, respectively. If the total sum is
positive, the rate of downward collisions is lower than the rate
of upward collisions. The difference in energy is assumed to be
radiated away, leading to net cooling. The contribution to the
cooling is calculated in each radial bin. While this approach may
be valid for lines that are optically thin throughout the CSE, the
fact that no description of the optical depth is included may be
problematic at the very high optical depths of the majority of the
H2 O-transitions. The net cooling assumes that the lost energy
leaves the radial bin (and CSE). For very high optical depths,
however, the radiated energy may be re-absorbed – either in a
radial bin further out, or possibly still in the same radial bin.
This would feed energy back into the envelope and reduce the
net cooling. The current implementation may hence overestimate
the amount of line cooling from H2 O.
This problem could possibly be solved by simply scaling the
contribution to the cooling in Eq. 7 by the escape probability
(1−e−τ )/τ. The implementation of this in the code is however not
trivial. The optical depth depends on the direction and is affected
by the surrounding density and velocity profiles. Since the code
only works along the radial direction, an angle-averaged optical
depth τ̄ would have to be calculated at each radial point, which is
not straight-forward. We are currently working on this problem,
trying to address the issue of properly including radiative line
cooling into the code.
Note that this does not only affect the cooling due to H2 O.
In principle CO can also reach high optical depths, and in carbon AGB stars cooling due to HCN lines affect the temperature
structure in the inner CSE in a very similar way to H2 O in Mtype AGB stars. Including line cooling correctly in the radiativetransfer codes, and identifying any potentially missed heating
(or cooling mechanisms) is essential for a complete understanding of the physical conditions in the inner CSEs of AGB stars.
This in turn affects chemical and dynamical models of the inner
Article number, page 8 of 17
winds, and our understanding of the evolution of the star on the
AGB in general.
5.2. The velocity profiles
Although not very well constrained, we derive comparatively
shallow velocity profiles for all sources, with β = 1.5 ± 1.0. For
IK Tau, Decin et al. (2010c) derive a β = 1 − 1.8. The velocity
profiles derived here and by Decin et al. (2010c) are consistent
with measurements of maser lines in the CSE of IK Tau (Bains
et al. 2003). The momentum equation for IK Tau on the other
hand gives β = 0.6 (Decin et al. 2010c). Khouri et al. (2014a)
adopt a β = 1.5 to describe the velocity profile in W Hya, and
find evidence that higher values may fit the high-J transitions of
CO better. Note that using the upper-state energy Eup as a measure of the distance in the CSE and the line width to constrain
the velocity profile as done by Justtanont et al. (2012) can be
misleading. For R Dor the measured line width vs. Eup for all
molecules detected in the HIFISTARS observations implies that
R Dor has a decelerating wind (Justtanont et al. 2012), showing
the importance of using full radiative transfer in order to derive
correct velocity profiles.
All measurements indicate that the wind follows a more shallow profile than generally predicted by dynamical models solving the coupled momentum equations of the dust and gas (e.g.,
Decin et al. 2006; Ramstedt et al. 2008; Decin et al. 2010c). Note
however, that Ramstedt et al. (2008) derive a velocity profile for
IK Tau that is consistent with the results by Bains et al. (2003),
showing that it is possible to derive velocity profiles from dynamical models that are consistent with the observed, shallow
profiles. At the same time this shows the large uncertainty in the
dynamical models, likely due to a sensitive dependence on the
input parameters, and the assumption of a fully momentum coupled wind. The choice of υg,i does not significantly affect our results. The observed lines are emitted from too far out in the wind
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
5.3. H2 O abundances
-2.5
log(f(H2O))
R Dor
o-H 2O
-4
-3
-3.5
-4.5
-4
-5
-4.5
15
15.4
15
R Cas
log(f(H2O))
o-H 2O
-4.5
-4.5
-5
-5
-5.5
15 15.4 15.8
14.6
TX Cam
o-H 2O
-4.6
log(f(H2O))
-3
15.4
p-H 2O
-4
14.6
15 15.4 15.8
p-H 2O
-5
-4
-5.4
-5
-3
16
16.5
15.5
IK Tau
o-H 2O
-3.5
-3.5
-4
-4
-4.5
-4.5
-5
15
For all sources we derive total H2 O abundances between (0.3 −
−4.0) × 10−4 relative to H2 (at the inner radius of our model
CSE, i.e. Ri ). Previous modelling of ISO observations of o-H2 O
resulted in the same o-H2 O abundances for R Dor and IK Tau,
while the values for R Cas and TX Cam were factors 5 and 10
higher, respectively. For IK Tau, Decin et al. (2010c) derive a
total H2 O abundance of 6.6 × 10−5 , uncertain by a factor of 2.
Within our uncertainties we just manage to meet the value derived by Decin et al. (2010c). However, they use a mass-loss
rate that is higher by ≈50% than our value, likely resulting in a
lower H2 O abundance. For the M-type AGB star W Hya, previously derived H2 O abundances are 8 × 10−4 and 3 × 10−4 (at radii
smaller and larger than 4.5 × 1014 cm, respectively; Barlow et al.
1996) ,and 9×10−4 (Khouri et al. 2014b). For non-LTE chemical
models, the predicted H2 O abundance in the inner CSE (< 5 R∗ )
of M-type AGB stars is 4 × 10−4 relative to H2 , while LTE models predict H2 O abundances closer to 7 × 10−5 (using TX Cam
as an example; Cherchneff 2006). Non-LTE chemical models of
IK Tau predict H2 O abundances of ≈ 2 × 10−4 at 6 R∗ (Gobrecht
et al. 2016), consistent with our value derived here. Although the
H2 O abundances derived here and in other publications based
on radiative-transfer modelling cover a large range, values of a
few times 10−4 appear to be an upper limit. Taken at face value,
and assuming that H2 O abundances remain largely unaffected by
processes in the intermediate wind, the results here favour the
formation of H2 O under non-LTE conditions in the inner wind.
However, within the uncertainties, the derived abundances seem
also to be consistent with the formation of H2 O under equilibrium conditions at 1 R∗ . The derived ortho- to para-H2 O ratio
is very uncertain, but is generally consistent with a value of 3,
implying formation of H2 O under warm conditions.
-5.8
15.5
log(f(H2O))
p-H 2O
16
17
log(radius) [cm]
15
16
16.5
p-H 2O
16
17
log(radius) [cm]
Fig. 7. χ2 -maps of the o-H2 O (left) and p-H2 O (right) model grids for
R Dor , R Cas , TX Cam , and IK Tau (top to bottom). The cross marks
the best-fit model using the H2 O radius as a free parameter, the circle
the best-fit model using RNK .
to effectively constrain the wind velocity at the inner radius. Any
reasonable changes in υg,i would not change the derived β values, but would mainly affect the energy balance in the inner CSE.
However, compared to the uncertainty in the treatment of the line
cooling, this effect is small.
5.4. Discrepancies between models and observations
Although the 1D radiative-transfer models generally reproduce
the overall line shapes (line-width and double-peaked, flattopped, parabolic, or triangular lines), it is clear that deviations
from these simple profiles are not reproduced. In addition to
over-resolved low-J lines in CO, asymmetries between the redand blue-shifted sides of the lines, and bumps and additional
peaks (e.g. in R Dor and R Cas, CO(6 − 5) at ≈3km s−1 ), are
not reproduced. In the H2 O lines the self-absorption on the blue
side due to the high optical depths of the lines is generally well
reproduced, however also with some deviations.
These differences may be caused by several effects. Varying mass-loss rates, velocity profiles, and photodissociation efficiencies will affect the spatial density distribution of the circumstellar wind, and the fractional abundance distribution of
the molecules. This will change the optical depths of the lines
and the excitation conditions. Such effects could, in principle,
be included in the 1D radiative transfer. However, effects due
to the three dimensional structure may have an equal, or even
stronger, effect on the observed lines. These include asymmetric winds, disks and tori, and clumpiness of the circumstellar
matter. Shocks in the inner wind and asymmetric illumination
of the CSE due to convection cells on the stellar surface and atmospheric molecular absorption bands can also strongly affect
the observed line shapes. Since the beginning of science observations with ALMA (Atacama Large Millimeter/submillimeter
Array), an increasingly complex picture of the inner winds of
AGB stars is being established, including the effects mentioned
above. VLT-SPHERE observations in the optical of R Dor reArticle number, page 9 of 17
A&A proofs: manuscript no. aa28310-16
solve the stellar disk, and show clear signs of an irregular brightness distribution from the stellar surface due to convection cells
(Khouri et al. in preparation).
5.5. Comparison to radiative transfer with GASTRoNOoM
Solving the molecular line radiative transfer for CSEs around
AGB stars encounters several physical (e.g. energy balance, radiation fields, velocity profiles, molecular data) and numerical
(e.g. modelling strategies, matrix inversion, optical depths) problems that have to be solved. As such, the number of advanced,
non-LTE radiative-transfer codes in use is limited. This is unfortunate, since this makes benchmarking, and comparison and verification of model results difficult. One of the radiative-transfer
codes that approaches the modelling of AGB CSEs in a similar
way to our code is GASTRoNOoM (Decin et al. 2006, 2007,
2008).
The estimate of the mass-loss rate for IK Tau based on GASTRoNOoM lies within 50% of our results (Decin et al. 2010c).
Khouri et al. (2014a) derive a mass-loss rate for W Hya of
1.5 × 10−7 M yr−1 , compared to 1.0 × 10−7 M yr−1 in our previous modelling (Maercker et al. 2008). Based on a grid of models
using GASTRoNOoM, De Beck et al. (2010) derive a formula to
estimate the mass-loss rates from AGB stars based on the intensities of the CO lines. Using their formula results in mass-loss
rates that are less than a factor two different from the values
derived here. This is well within the limit of the absolute uncertainty expected from this modelling method (Ramstedt et al.
2008). Compared to what we find in our modelling, the derived
H2 O abundances using GASTRoNOoM appear to be lower by
a factor of two for IK Tau. Comparing the results by Khouri
et al. (2014b) with Maercker et al. (2008), they are a factor of
five lower for W Hya. However, the absolute uncertainties are
relatively large, and a more systematic comparison between the
two radiative-transfer codes is necessary to identify whether the
discrepancy in H2 O abundances is due to numerical differences
in the codes, or simply reflects the uncertainty and difficulty in
modelling H2 O line emission.
6. Conclusions
We have successfully modelled CO and H2 O lines observed
towards four M-type AGB stars, including spectrally resolved
ground-based and HIFI observations for CO, spectrally resolved
HIFI observations of o-H2 O and p-H2 O, and spectrally unresolved observations of CO and H2 O with PACS. These are the
first models of a larger sample of sources with spectrally resolved H2 O line profiles. We derive H2 O abundances, o/p-H2 O
ratios, the sizes of the H2 O line emitting regions, velocity and
temperature profiles, and attempt to include full H2 O line cooling in the energy balance in the radiative transfer. Based on the
modelling we arrive at following conclusions.
– Our modelling indicates that the winds around these four Mtype AGB stars have a comparatively shallow acceleration
profile, in contrast to what is generally expected from dynamical models of dust-driven winds. However, we also note
that the widths of the line profiles only moderately constrain
the velocity profile.
– Although we managed to include H2 O line cooling in the
energy balance for the low mass-loss rate objects R Dor and
R Cas, this required an unphysical description of the dust
expansion velocity in order to counter-balance the extreme
cooling from H2 O in the inner CSE. This implies that the
Article number, page 10 of 17
physical processes that describe the heating and cooling in
the inner envelope are not completely understood and/or that
the formal implementation of line cooling is not correct.
– We derive generally high H2 O abundances, up to a few times
10−4 relative to H2 . Within the uncertainties, all derived
abundances are consistent with both NLTE and LTE abundances derived from chemical models, emphasizing the importance of improved radiative transfer models to reduce uncertainties on abundances derived from observations.
– The derived o/p-ratios are uncertain, however consistent with
a value of three, indicating formation of H2 O in the warm,
inner CSE.
Computational limitations currently do not allow us to selfconsistently solve the physics and dynamics throughout the CSE
in three dimensions. 1D radiative-transfer models as presented
here are important for constraining the basic physical parameters
of the envelopes (e.g., temperature, velocity, average mass-loss
rates). These can be used as input for 3D models (e.g. LIME;
Brinch & Hogerheijde 2010) to study the effect of structure in
three dimensions. In order to arrive at a self-consistent model
that fully describes the physical conditions throughout the CSE,
however, it is important to solve the problem of radiative line
cooling, in particular for H2 O.
Acknowledgements. M.M. has received funding from the People Programme
(Marie Curie Actions) of the EU’s FP7 (FP7/2007-2013) under REA grant agreement No. 623898.11. HO acknowledges financial support from the Swedish Research Council. M.M. would like to thank Fredrik Schöier for his contribution at
the beginning of this project, his advice and support. Sadly he could not be here
to see the results.
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Article number, page 11 of 17
A&A proofs: manuscript no. aa28310-16
Appendix A: Observed and model line intensities,
and model line profiles
Article number, page 12 of 17
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
Table A.1. Observed and modelled CO lines.
Transition
J-level
Ground based
CO(1 − 0)
CO(2 − 1)
CO(3 − 2)
CO(4 − 3)
λ
[GHz]
Eup
[K]
Iobs
115.3
230.5
345.8
461.0
3.85
11.54
23.07
38.45
5.00
41.6
70.4
–
J-level
HIFI
CO(6 − 5)
CO(10 − 9)
CO(16 − 15)
[GHz]
[K]
691.5
1152.0
1841.3
80.74
211.40
522.48
[µm]
[K]
186.00
173.63
162.81
153.27
137.20
124.19
118.58
108.76
403.46
461.05
522.48
587.72
729.68
886.90
971.23
1151.32
J-level
PACS
CO(14 − 13)
CO(15 − 14)
CO(16 − 15)
CO(17 − 16)
CO(19 − 18)
CO(21 − 20)
CO(22 − 21)
CO(24 − 23)
R Dor
Imod
∆
[K km s−1 ]
5.52
38.5
72.4
–
1.10
0.93
1.03
–
Iobs
8.40
32.1
100
89.6
[K km s−1 ]
16.8
15.9
11.6
12.5
13.8
13.8
2.78
2.96
–
3.26
–
3.55
–
–
8.21
35.1
68.3
85.7
0.98
1.09
0.68
0.96
Iobs
0.74
0.87
1.19
17.2
12.8
6.76
7.74
8.87
7.69
1.45
1.53
1.70
1.70
1.55
1.35
3.16
–
1.65
1.70
1.74
1.75
1.72
1.63
1.57
–
13.0
43.7
87.4
95.7
Iobs
0.90
0.72
1.25
0.64
0.45
0.69
1.14
16.6
8.15
–
8.19
9.86
–
2.06
2.07
2.07
1.93
–
8.77
3.18
1.40
1.96
2.06
2.14
2.20
–
2.21
2.17
2.03
32.0
74.1
110
130
0.97
0.78
0.88
1.00
[K km s−1 ]
0.49
1.21
–
12.0
9.45
15.9
[10−16 W m−2 ]
1.14
1.11
1.02
1.03
1.11
1.21
0.50
–
IK Tau
Imod
∆
[K km s−1 ]
33.0
95.0
125
130
[K km s−1 ]
[10−16 W m−2 ]
1.14
1.01
–
0.86
–
0.94
–
–
TX Cam
Imod
∆
[K km s−1 ]
14.5
60.6
70.0
149
[K km s−1 ]
[10−16 W m−2 ]
2.43
2.94
–
3.77
–
3.77
–
–
R Cas
Imod
∆
[K km s−1 ]
10.9
13.7
14.1
0.91
1.45
0.89
[10−16 W m−2 ]
0.95
1.00
1.03
1.14
–
0.25
0.68
1.45
3.63
4.55
3.93
4.06
4.06
3.53
5.79
4.16
2.85
3.03
3.18
3.30
3.44
3.46
3.42
3.27
0.79
0.67
0.81
0.81
0.85
0.98
0.59
0.79
Table A.2. Observed and modelled ortho-H2 O lines.
Transition
JKa ,Kc -level
HIFI
o-H2 O (110 − 101 )
o-H2 O (532 − 441 )
o-H2 O (312 − 303 )
o-H2 O (312 − 221 )
o-H2 O (321 − 312 )
o-H2 O (302 − 212 )
JKa ,Kc -level
PACS
o-H2 O (221 − 212 )
o-H2 O (212 − 101 )
o-H2 O (734 − 725 )
o-H2 O (532 − 523 )
o-H2 O (845 − 752 )
o-H2 O (514 − 505 )
o-H2 O (836 − 743 )
o-H2 O (423 − 414 )
o-H2 O (945 − 936 )
o-H2 O (725 − 716 )
o-H2 O (936 − 927 )
o-H2 O (432 − 423 )
o-H2 O (734 − 643 )
o-H2 O (221 − 110 )
o-H2 O (634 − 625 )
o-H2 O (625 − 616 )
o-H2 O (643 − 634 )
o-H2 O (836 − 827 )
o-H2 O (616 − 505 )
o-H2 O (927 − 918 )
o-H2 O (423 − 312 )
o-H2 O (752 − 743 )
o-H2 O (550 − 541 )
o-H2 O (321 − 212 )
o-H2 O (707 − 616 )
o-H2 O (827 − 818 )
o-H2 O (330 − 303 )
o-H2 O (330 − 221 )
o-H2 O (716 − 625 )
o-H2 O (625 − 514 )
o-H2 O (818 − 707 )
o-H2 O (432 − 321 )
λ
[GHz]
Eup
[K]
Iobs
556.9
620.7
1097.4
1153.1
1162.9
1716.8
60.96
732.06
249.43
249.43
305.24
196.77
12.3
–
18.6
51.6
19.3
–
[µm]
[K]
180.49
179.53
166.81
160.51
159.05
134.94
133.55
132.41
129.34
127.88
123.46
121.72
116.78
108.07
104.09
94.64
92.81
82.98
82.03
81.41
78.74
77.76
75.91
75.38
71.95
70.70
67.27
66.44
66.09
65.17
63.32
58.70
194.09
114.38
1211.96
732.06
1615.32
574.73
1447.57
432.15
1957.06
1125.71
1845.82
550.35
1211.96
194.09
933.73
795.51
1088.75
1447.57
643.49
1729.29
432.15
1524.86
1067.68
305.24
843.47
1274.17
410.65
410.65
1013.20
795.51
1070.68
550.35
R Dor
Imod
∆
[K km s−1 ]
8.72
–
13.7
68.3
13.6
–
0.71
–
0.74
1.32
0.70
–
[10−16 W m−2 ]
5.92
14.3
2.32
4.27
4.87
6.48
10.1
9.88
–
3.07
2.72
9.33
15.7
32.7
5.96
11.3
8.60
5.74
–
–
50.4
6.16
13.7
51.4
30.4
19.0
51.9
62.8
42.1
40.7
52.0
54.3
5.51
14.1
1.35
3.16
7.54
6.38
18.2
8.10
–
2.35
1.29
6.65
16.7
27.8
5.43
8.99
6.68
5.42
–
–
37.1
5.42
9.65
57.2
36.9
11.4
32.0
50.6
48.6
36.3
42.9
46.5
0.93
0.99
0.58
0.74
1.55
0.99
1.80
0.82
–
0.77
0.47
0.71
1.06
0.85
0.91
0.80
0.78
0.94
–
–
0.74
0.88
0.70
1.11
1.21
0.60
0.62
0.81
1.16
0.89
0.83
0.86
Iobs
8.36
–
13.1
24.9
10.4
–
R Cas
Imod
∆
[K km s−1 ]
3.87
–
6.36
23.1
5.02
–
0.46
–
0.49
0.93
0.48
–
[10−16 W m−2 ]
2.65
7.32
0.33
1.07
0.56
1.71
–
3.28
–
–
–
3.17
–
13.3
–
3.05
1.60
1.16
9.97
1.65
16.3
–
1.99
20.9
–
–
13.8
17.8
–
–
–
14.2
1.25
3.39
0.32
0.86
0.61
1.70
–
2.01
–
–
–
1.61
–
6.76
–
2.52
1.72
1.44
9.85
1.04
11.0
–
2.16
13.2
–
–
7.05
11.6
–
–
–
13.1
0.47
0.46
0.97
0.81
1.08
1.00
–
0.61
–
–
–
0.51
–
0.51
–
0.83
1.07
1.24
0.99
0.63
0.68
–
1.09
0.63
–
–
0.51
0.65
–
–
–
0.92
Iobs
6.71
–
7.24
10.6
4.91
–
TX Cam
Imod
∆
[K km s−1 ]
2.45
–
4.68
13.2
3.07
–
Iobs
0.36
–
0.65
1.24
0.62
–
[10−16 W m−2 ]
3.77
8.56
–
0.79
–
–
–
2.51
–
–
–
1.60
–
10.2
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1.00
2.56
–
0.63
–
–
–
1.58
–
–
–
1.34
–
4.94
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
11.4
18.2
15.7
28.4
15.1
32.2
IK Tau
Imod
∆
[K km s−1 ]
6.8
28.2
14.1
34.4
11.2
30.1
0.59
1.55
0.89
1.21
0.74
0.93
[10−16 W m−2 ]
0.27
0.30
–
0.80
–
–
–
0.63
–
–
–
0.84
–
0.48
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
5.93
10.0
2.52
4.20
1.94
6.37
4.45
9.47
2.61
5.82
2.23
9.86
7.48
24.5
10.8
12.4
10.3
9.33
9.44
29.8
7.19
11.4
36.6
18.0
14.7
–
–
–
–
–
–
–
2.14
4.18
1.31
2.21
2.25
4.65
5.44
4.59
1.56
3.16
1.75
5.00
6.56
10.2
6.23
8.22
7.40
8.08
6.35
17.4
8.07
10.4
22.6
18.5
12.9
–
–
–
–
–
–
–
0.36
0.42
0.52
0.53
1.16
0.73
1.22
0.48
0.60
0.54
0.79
0.51
0.88
0.41
0.58
0.66
0.72
0.87
0.67
0.58
1.12
0.91
0.62
1.03
0.88
–
–
–
–
–
–
–
Article number, page 13 of 17
A&A proofs: manuscript no. aa28310-16
Table A.3. Observed and modelled para-H2 O lines.
JKa ,Kc -level
PACS
p-H2 O (413 − 404 )
p-H2 O (735 − 642 )
p-H2 O (624 − 615 )
p-H2 O (431 − 422 )
p-H2 O (413 − 322 )
p-H2 O (404 − 313 )
p-H2 O (937 − 844 )
p-H2 O (946 − 853 )
p-H2 O (524 − 515 )
p-H2 O (542 − 533 )
p-H2 O (744 − 735 )
p-H2 O (606 − 515 )
p-H2 O (835 − 744 )
p-H2 O (726 − 717 )
p-H2 O (853 − 844 )
p-H2 O (615 − 524 )
p-H2 O (651 − 642 )
p-H2 O (937 − 928 )
p-H2 O (551 − 624 )
p-H2 O (717 − 606 )
p-H2 O (524 − 413 )
p-H2 O (331 − 220 )
p-H2 O (808 − 717 )
p-H2 O (431 − 404 )
p-H2 O (826 − 735 )
p-H2 O (726 − 615 )
λ
[GHz]
Eup
[K]
Iobs
752.0
970.3
987.9
1113.3
1207.6
1717.0
1762.0
136.94
598.83
100.84
53.54
454.33
725.09
951.82
–
–
–
33.6
6.72
–
6.18
[µm]
[K]
187.11
169.74
167.03
146.92
144.52
125.35
118.41
117.68
111.63
94.21
90.05
83.28
81.69
81.22
80.56
78.93
76.42
73.61
71.79
71.54
71.07
67.09
63.46
61.81
60.16
59.99
396.38
1175.03
867.25
552.26
396.38
319.48
1749.88
1929.22
598.83
877.81
1334.81
642.69
1510.93
1020.93
1806.97
781.12
1278.54
1749.88
1067.67
843.81
598.83
410.36
1070.54
552.26
1749.82
1414.18
R Dor
Imod
∆
[K km s−1 ]
–
–
–
22.9
5.99
–
5.97
–
–
–
0.68
0.89
–
0.97
[10−16 W m−2 ]
2.61
2.74
1.08
3.34
11.6
20.2
3.30
–
6.18
7.38
–
31.9
–
–
–
29.1
–
–
–
25.3
29.4
50.8
24.8
25.8
19.3
31.7
2.66
4.05
1.05
3.66
19.8
25.9
1.86
–
5.82
5.01
–
31.7
–
–
–
31.5
–
–
–
34.1
35.4
35.9
31.5
19.1
22.0
30.5
1.02
1.48
0.97
1.10
1.71
1.28
0.56
–
0.94
0.68
–
0.99
–
–
–
1.08
–
–
–
1.35
1.20
0.71
1.27
0.74
1.14
0.96
Iobs
R Cas
Imod
∆
[K km s−1 ]
–
–
–
19.8
3.36
–
–
–
–
–
10.4
1.98
–
–
0.74
0.53
–
1.05
3.22
–
–
–
1.92
1.49
–
5.81
–
–
–
–
–
–
–
–
6.91
–
–
–
–
–
0.95
0.58
–
1.09
4.29
–
–
–
1.77
1.29
–
7.33
–
–
–
–
–
–
–
–
8.91
–
–
–
–
–
0
0.5
0.94
–
–
0.82
2.63
0.88
–
–
0.97
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
4
2
-20
0
20
velocity [km/s]
-20
0
20
velocity [km/s]
CO(6-5), ∆ : 0.4
CO(10-9), ∆ : 0.7
CO(16-15), ∆ : 1.1
T mb [K]
T mb [K]
0.5
[10−16 W m−2 ]
2.28
1.66
2.64
4.20
8.46
15.0
1.83
1.53
7.28
–
5.29
20.2
4.79
9.42
4.60
19.8
7.63
5.54
6.20
15.1
2.17
3.21
1.72
2.93
6.62
7.59
2.51
1.95
6.12
–
5.91
14.6
82.4
9.68
5.76
16.7
9.08
6.74
0.62
17.0
0.95
1.93
0.65
0.70
0.78
0.51
1.37
1.27
0.84
–
1.12
0.72
1.72
1.03
1.25
0.84
1.19
1.22
0.10
1.13
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
CO(4-3), ∆ : 1
4
2
-20
0
20
velocity [km/s]
0.5
0
0
-20
0
20
velocity [km/s]
0.37
–
–
0.42
0.42
2.03
–
–
0.70
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
0.82
1.93
0.72
0.68
–
1.11
3.57
1
1
0
0.35
–
–
0.34
1.11
1.78
–
–
0.68
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
10.9
33.7
17.0
16.5
–
3.01
7.49
0
-20
0
20
velocity [km/s]
0.5
13.2
17.5
23.7
24.4
–
2.70
2.10
IK Tau
Imod
∆
[K km s−1 ]
6
0
0
1
T mb [K]
1
–
–
–
0.40
–
–
–
Iobs
[10−16 W m−2 ]
6
1.5
T mb [K]
T mb [K]
T mb [K]
0.2
–
–
–
5.31
–
–
–
CO(3-2), ∆ : 0.7
2
0.4
1.29
1.10
–
1.04
1.33
–
–
–
0.92
0.87
–
1.26
–
–
–
–
–
–
–
–
1.29
–
–
–
–
–
TX Cam
Imod
∆
[K km s−1 ]
–
–
–
13.2
–
–
–
[10−16 W m−2 ]
CO(2-1), ∆ : 1.1
CO(1-0), ∆ : 1
–
–
–
0.53
0.59
–
–
Iobs
T mb [K]
Transition
JKa ,Kc -level
HIFI
p-H2 O (211 − 202 )
p-H2 O (524 − 431 )
p-H2 O (202 − 111 )
p-H2 O (111 − 000 )
p-H2 O (422 − 413 )
p-H2 O (533 − 606 )
p-H2 O (633 − 624 )
-20
0
20
velocity [km/s]
-20
0
20
velocity [km/s]
Fig. A.1. Best-fit CO models for R Cas. The blue histograms are the observations. The red lines are the model lines, the green lines are the model
lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the 3LSR = 24.5 km s−1 .
Article number, page 14 of 17
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
CO(2-1), ∆ : 0.7
CO(1-0), ∆ : 0.9
CO(3-2), ∆ : 1.2
3
CO(4-3), ∆ : 0.6
6
0.2
0
1
0
-50
0
50
velocity [km/s]
1
-50
0
50
velocity [km/s]
4
2
0
0
CO(6-5), ∆ : 0.5
-50
-50
0
50
velocity [km/s]
0
50
velocity [km/s]
CO(10-9), ∆ : 1.2
0.6
0.4
T mb [K]
T mb [K]
2
T mb [K]
[K]
mb
0.4
T mb [K]
2
0.6
T
T mb [K]
0.8
0.4
0.2
0.2
0
0
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
Fig. A.2. Best-fit CO models for TX Cam.The blue histograms are the observations. The red lines are the model lines, the green lines are the model
lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the 3LSR = 12.0 km s−1 .
-50
-2
0
50
velocity [km/s]
CO(6-5), ∆ : 0.9
0.6
0.2
0
CO(10-9), ∆ : 1.5
0.2
0
-50
0
50
velocity [km/s]
-0.2
2
-2
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
2
0
-50
0
50
velocity [km/s]
-2
-50
0
50
velocity [km/s]
CO(16-15), ∆ : 0.9
1
0.4
T mb [K]
T mb [K]
-50
CO(4-3), ∆ : 1
6
4
0
0.6
0.4
-0.2
0
T mb [K]
-0.5
T mb [K]
[K]
0
CO(3-2), ∆ : 0.9
6
4
2
mb
T
T mb [K]
1
0.5
CO(2-1), ∆ : 0.8
4
T mb [K]
CO(1-0), ∆ : 1
1.5
0.5
0
-0.5
-50
0
50
velocity [km/s]
Fig. A.3. Best-fit CO models for IK Tau.The blue histograms are the observations. The red lines are the model lines, the green lines are the model
lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the 3LSR = 34.0 km s−1 .
Article number, page 15 of 17
A&A proofs: manuscript no. aa28310-16
o-H 2O(1 10-1 01), ∆ : 0.5
o-H 2O(3 12-3 03), ∆ : 0.5
o-H 2O(3 12-2 21), ∆ : 0.9
o-H 2O(3 21-3 12), ∆ : 0.5
1
1
0.5
T mb [K]
0.4
2
T mb [K]
0.6
T mb [K]
T mb [K]
0.8
1
0.5
0.2
0
-40 -20 0 20 40
velocity [km/s]
0
0
0
-40 -20 0 20 40
velocity [km/s]
-40 -20 0 20 40
velocity [km/s]
-40 -20 0 20 40
velocity [km/s]
p-H 2O(1 11-0 00), ∆ : 0.5
p-H 2O(4 22-4 13), ∆ : 0.6
2
0.4
T mb [K]
T mb [K]
1.5
1
0.5
0.2
0
0
-40 -20 0
20 40
velocity [km/s]
-40 -20 0
20
velocity [km/s]
40
Fig. A.4. Best-fit o-H2 O and p-H2 O models of the HIFI Lines for R Cas. The blue histograms are the observations. The red lines are the model
lines, the green lines are the model lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the
3LSR = 24.5 km s−1 .
o-H 2O(3 12-3 03), ∆ : 0.7
o-H 2O(3 12-2 21), ∆ : 1.2
0.3
0.3
0.6
0.2
0.1
0.2
0.1
0.3
0.4
0.2
0.2
0.1
0
0
0
0
o-H 2O(3 21-3 12), ∆ : 0.6
T mb [K]
0.8
T mb [K]
0.4
T mb [K]
T mb [K]
o-H 2O(1 10-1 01), ∆ : 0.4
0.4
-0.1
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
p-H 2O(1 11-0 00), ∆ : 0.4
T mb [K]
0.6
0.4
0.2
0
-50
0
50
velocity [km/s]
Fig. A.5. Best-fit o-H2 O and p-H2 O models of the HIFI Lines for TX Cam. The blue histograms are the observations. The red lines are the model
lines, the green lines are the model lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the
3LSR = 12.0 km s−1 .
Article number, page 16 of 17
M. Maercker et al.: A HIFI view on circumstellar H2 O in M-type AGB stars
o-H 2O(5 32-4 41), ∆ : 1.6
o-H 2O(1 10-1 01), ∆ : 0.6
o-H 2O(3 12-3 03), ∆ : 0.9
o-H 2O(3 12-2 21), ∆ : 1.2
0.8
1.5
1
0.5
0.4
0.2
1
0.5
0
0
0
0
T mb [K]
0.2
0.6
T mb [K]
T mb [K]
T mb [K]
1.5
0.4
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
o-H 2O(3 21-3 12), ∆ : 0.7
o-H 2O(3 02-2 12), ∆ : 0.9
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
p-H 2O(2 02-1 11), ∆ : 0.9
p-H 2O(1 11-0 00), ∆ : 0.6
1.5
0.6
T mb [K]
T mb [K]
0.8
0.4
0.2
1
0.5
0
0
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
p-H 2O(2 11-2 02), ∆ : 0.7
p-H 2O(5 24-4 31), ∆ : 1.2
0.6
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
p-H 2O(5 33-6 06), ∆ : 0.5
p-H 2O(6 33-6 24), ∆ : 2.8
0.4
0.5
0
0
0
0.5
0
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
0.4
T mb [K]
T mb [K]
0.5
1
1
T mb [K]
0.2
T mb [K]
T mb [K]
T mb [K]
1
0.4
0.2
0
-0.2
0.2
0
-0.2
-50
0
50
velocity [km/s]
-50
0
50
velocity [km/s]
Fig. A.6. Best-fit o-H2 O and p-H2 O models of the HIFI Lines for IK Tau. The blue histograms are the observations. The red lines are the model
lines, the green lines are the model lines scaled to the same integrated intensities as the observations. The velocities are given with respect to the
3LSR = 34.0 km s−1 .
Article number, page 17 of 17